To generate the persistence image corresponding to a persistence diagram represented as a multiset of points \((b,d)\) , the points are first transformed to give a multiset \(B\)  of birth and persistence coordinates \((b,d-b)\)  (for extended persistence, we require a slightly different formulation – see below). We note that the persistent image formulation of [1]} ignores all infinite persistent features. A persistence surface in \({R}^2\rightarrow {R}\)  is then defined as the weighted sum of kernels applied to each birth/persistence coordinate
\(f(x,y) = \sum _{(b,p)\in B} g(b,p)h(x,y;b,p)\) 
